week 2 assignment

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ASSIGNMENT 1 1 Assignment 1 - Week 2 (MATH) Anderson A. Peoples Jr. TLMT 601, Winter 2024 American Public University Professor Emmet Fritch 1/14/2024

Assignment 1 2 Mathematics in Transportation Economics 1. In trip calculation, it is observed that a Wal-Mart store driver successfully made a total of 120 trips in a given period of time. During field calculation, it is shown that the calculated number of trips is actually 144. What is the value of the adjustment factor? (14 points) Answer: Kij=Tij(observed)/Tij(calculated) Kij = adjustment factor Tij(observed) = 120 Tij(calculated) = 144 Kij= 120/144 Kij = 0.83333333 2. It is shown that the population of New York City, NY is much greater than that of Irvington, NJ. Employment opportunities, malls, social activities and tourist sites in New York City are therefore more than that in Irvington. If attractiveness for New York and Irvington are therefore 1,600 and 160 respectively and if the calculated impedance of migration is known to be 1.57, based on Gravity-Based model, estimate in demands, the number of people who travel between Irvington, NJ and New York City per week. (14 points) Answer: V AB= NA NB I AB Vab = Na*Nb*Iab

Assignment 1 3 Vab = demand for transportation between New York and Irvington Na = New York City=1600 Nb = Irvington=160 Travel impedance = 1.57 Vab = 1600x160x1.57 = 401,920 people per week 3. Elasticity can be defined as percentage change in demand for a 1% change in decision attribute. For linear aggregate demand, what is the mathematical representation/formula for this statement? You must define the parameters you choose to use for this answer. (14 points) Answer: x = mode type, trip purpose, time of day, trip length, trip-maker characteristics, existing level of factor V = the point elasticity of travel demand 4. In the City of Joplin, due to weather devastation and hurricane effects, the cost of parking in the local Square has increased by 15%. This change has not only reduced the number of vehicles that travel to the Square by 10%, but it has also forced the inhabitants

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Assignment 1 4 of Joplin to use buses. Bus trips have therefore increased to 25%. With respect to the cost of parking in the local Square, determine the elasticity of vehicle traffic. (14 points) Answer: Initial parking price = p1 Final parking price =p2=1.15p1 Initial transit demand = Vt1 Final transit demand=Vt2=1.25Vt1 Initial auto demand =Va1 Final auto demand=Va2=0.90Va1 eTP=(Va2-Va1)(p1+p2)/2/(p2-p1)(Va1+Va2)/2 =(.90Va1-Va1)(p1+1.15p1)/2/{(1.15p1-p1)(Va1+.90Va1)/2} = -0.75 5. In your own words, describe the meaning of average cost. You normally buy a crate of wine for $75. One crate has 8 bottles of wine. After a month, the store clerk informs you that the same crate of wine now costs $82. However, there are 10 bottles in a crate. To the nearest cent, determine the average cost of the crate from last month to now. (14 points) Answer:

Assignment 1 5 The average cost is equal to the average total cost, average fixed cost and average variable cost. The average total cost (ATC), is the total cost associated with 1 unit of output. It is calculated as the ratio of the total cost to the output: ATC = TC /V, where TC is the total cost and V is the volume (output). The average fixed cost (AFC), is the fixed cost associated with 1 unit of output and is calculated as the ratio of the fixed cost to the output, AFC = FC /V. Similarly, the average variable cost is the cost of 1 unit of output and is calculated as the ratio of the variable cost to the output, AVC = VC /V. The concept of average costs is useful in the economic evaluation of transportation system improvements because it helps assess the cost impacts of improvements at a given supply level (TLMT 601-Transportation Economics: Math Tutorial Guide). 75/8 = $9.38 per bottle 82/10 = $8.20 per bottle $9.38-$8.20 = $1.18 difference in bottle cost 75-82 = -7, or a case has increased in cost by $7.00 6. In your own words, describe the meaning of marginal cost. You normally buy a crate of wine for $75. One crate has 8 bottles of wine. After a month, the store clerk informs you that the same crate of wine now costs $82. However, there are 10 bottles in a crate. To the nearest cent, determine the marginal cost for one additional bottle of wine now. (15 points) Answer:

Assignment 1 6 The marginal cost of a transportation good or service is the incremental cost of producing an additional unit of output. The terms of incremental cost, differential cost, and marginal cost have essentially similar meaning but typically are used in contexts that have very subtle differences. Incremental cost is a small increase in cost. Differential cost is the ratio of a small increment of cost to a small increase in production output. Marginal cost analysis is relevant in transportation system evaluation because an agency may seek the incremental cost changes in response to planned or hypothetical production of an additional unit of output with respect to facility construction, preservation, or operations. Marginal cost and average cost can differ significantly. For example, suppose that an agency spends $10 million to build a 10-mile highway and $10.5 million to build a similar 11-mile highway, the average costs are $1 million and $0.954 million, respectively, but the marginal cost of the additional mile is $0.5 million. The expressions related to marginal cost are as follows: Marginal variable cost: MVC = ∂ VC ∂V Marginal total cost: MTC = ∂ TC ∂V = ∂ FC ∂V + ∂ VC ∂V = ∂ VC ∂V = MVC Like average cost, marginal cost concepts help an agency or shipper to evaluate the cost impacts of various levels of output or the additional cost impact of moving from a certain output level to another. (TLMT 601-Transportation Economics: Math Tutorial Guide). 75/8 = $9.38 per bottle 82/10 = $8.20 per bottle

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Assignment 1 7 $9.38-$8.20 = $1.18 difference in bottle cost 75-82 = -7, or a case has increased in cost by $7.00 7. In your own words, describe the meaning of unit travel. When traveling on a Greyhound bus, without intervention or obstruction, it is important to determine the unit travel time. If you leave Cleveland in a bus full of 30 passengers and arrive Cincinnati in 4 hours, what will be the average unit travel time in person minutes? (15 points) Answer. Unit in-vehicle travel time per traveler, U 1 = OCC × TT V where TT V is the average vehicular operating travel time and OCC is the average vehicle occupancy. In cases where the travel speeds of trucks and other commercial vehicles are significantly different from passenger vehicles, separate travel time estimates should be made for each vehicle class. (TLMT 601-Transportation Economics: Math Tutorial Guide). Assuming that 30 passengers include me, the average unit travel time will be 30 x 240 = 7200 without interruption. 4 hours = 240 minutes multiplied by 30 passengers.

Assignment 1 8 References Labi, S., & Sinha, K. C. (2007). Transportation Decision Making: Principle of Project Evaluation and Programming. Hoboken, New Jersey: John Wiley & Sons, Inc. TLMT601-Transportation Economics. Math Tutorial Guide. Problem Examples. Transportation Demand, Statistical Analysis of Economic Relations, Vehicle Operating Costs & Interest Calculation, Box

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